$(20$ pts $)$ In Lecture $1,$ we explored how dimensional analysis can simplify the study of drag force by reducing five parameters

$(F_D,A,V,,)$ into two nondimensional parameters. One student raised an interesting question: This analysis may possible

because we already know that drag force is related to factors such as area, velocity, viscosity, and density. What would happen

if one of these variables was accidentally omitted? Let's check this issue together.

$($a$)(10$ pts$)$ Perform dimensional analysis using only four parameters: $F_D,V,,$

$*$Hint: Use a reduction number $j=3$ to derive one nondimensional parameter $($i$.$e$.,k=1).$

$($b$)(10$ pts$)$ If the dimensional analysis results in a single nondimensional parameter, this value must remain constant. Prove

that the nondimensional parameter derived in part $($a$)$ remains constant, given that both the Reynolds number and the drag

coefficient are constant.

Please give handwritten answers and do not copy from previous answers. Thank u